U.S. patent application number 16/073936 was filed with the patent office on 2019-02-07 for thermally strengthened glass sheets having characteristic membrane stress homogeneity.
The applicant listed for this patent is Corning Incorporated. Invention is credited to Jeffrey John Domey, Dragan Pikula, Robert Wendell Sharps.
Application Number | 20190039936 16/073936 |
Document ID | / |
Family ID | 59398977 |
Filed Date | 2019-02-07 |
United States Patent
Application |
20190039936 |
Kind Code |
A1 |
Domey; Jeffrey John ; et
al. |
February 7, 2019 |
THERMALLY STRENGTHENED GLASS SHEETS HAVING CHARACTERISTIC MEMBRANE
STRESS HOMOGENEITY
Abstract
A glass sheet thermally strengthened such that at the first
major surface is under compressive stress; the sheet having an a
characteristic 2D autocorrelation matrix c(x,y) given by
c(x,y)=F.sup.-1(F(g)F (g)) where F is a 2D Fourier transform and
represents a complex conjugate operation and g is a high pass
filtered data array given by g(x,y)=F.sup.-1(F(f(1-F(h)) where h is
a spatial 2D low pass filter array and f is a square data array of
Shear 0 and Shear 45 data, taken over an area away from any
birefringence edge effects on the sheet, wherein an autocorrelation
peak maximum width of the matrix c(x,y) at 40% of peak height, for
the c(x,y) matrices from both the Shear 0 and Shear 45 data, is
between 1 and 5 mm.
Inventors: |
Domey; Jeffrey John;
(Elmira, NY) ; Pikula; Dragan; (Horseheads,
NY) ; Sharps; Robert Wendell; (Corning, NY) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Corning Incorporated |
Corning |
NY |
US |
|
|
Family ID: |
59398977 |
Appl. No.: |
16/073936 |
Filed: |
January 31, 2017 |
PCT Filed: |
January 31, 2017 |
PCT NO: |
PCT/US17/15736 |
371 Date: |
July 30, 2018 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62289334 |
Jan 31, 2016 |
|
|
|
62428531 |
Dec 1, 2016 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
C03B 27/016 20130101;
C03C 2204/08 20130101; C03C 23/007 20130101; C03B 27/048 20130101;
C03B 27/0413 20130101; C03B 29/08 20130101; C03B 35/24
20130101 |
International
Class: |
C03B 27/016 20060101
C03B027/016; C03B 27/04 20060101 C03B027/04; C03B 29/08 20060101
C03B029/08 |
Claims
1. A strengthened glass sheet, the sheet comprising first major
surface; a second major surface opposite the first major surface
and separated from the first major surface by a thickness t when
expressed in mm; a length of l when expressed in mm of at least 10;
a width of w when expressed in mm of at least 10; an interior
region located between the first and second major surfaces; and an
outer edge surface extending between and surrounding the first and
second major surfaces such that the outer edge surface defines a
perimeter of the sheet; wherein the sheet is thermally strengthened
such that at the first major surface is under compressive stress;
the sheet having an a characteristic 2D autocorrelation matrix
c(x,y) given by c(x,y)=F.sup.-1(F(g){circumflex over (F)}(g)) where
F is a 2D Fourier transform and represents the complex conjugate
operation and g is a high pass filtered data array given by
g(x,y)=F.sup.-1(F(f)(1-F(h))) where h is a spatial 2D low pass
filter array and f is a square data array of Shear 0 and Shear 45
data, taken over an area away from any birefringence edge effects
on the sheet, wherein an autocorrelation peak maximum width of the
matrix c(x,y) at 40% of peak height, for the c(x,y) matrices from
both the Shear 0 and Shear 45 data, is between 1 and 5 mm.
2. The sheet according to claim 1 wherein the autocorrelation peak
maximum width of the matrix c(x,y) at 40% of peak height, for the
c(x,y) matrices from both the Shear 0 and Shear 45 data, is between
1 and 4 mm.
3. The sheet according to claim 1 wherein the autocorrelation peak
maximum width of the matrix c(x,y) at 40% of peak height, for the
c(x,y) matrices from both the Shear 0 and Shear 45 data, is between
1 and 3 mm.
4. The strengthened glass sheet according to claim 1, wherein the
first major surface of the sheet has a roughness, measured over an
area on the first major surface of 10 .mu.m.times.10 .mu.m, is in
the range of from 0.05 nm to 0.5 nm Ra.
5. The strengthened glass sheet according to claim 1, wherein the
first major surface of the sheet has a roughness, measured over an
area on the first major surface of 10 .mu.m.times.10 .mu.m, is in
the range of from 0.05 nm to 0.3 nm Ra.
6. The strengthened glass sheet according to claim 1, wherein a
normalized standard deviation S.sub.n S n = s x _ ##EQU00004## of
membrane stress measurement samples taken through the first and
second major surfaces 12, 14 the sheet 10 in a series distributed
equally in the x and y directions, but not within a distance of 2.5
times the thickness of the sheet to the outer edge surface 16, for
number of samples N=100, is less than or equal to 0.02.
7. A strengthened glass sheet according to claim 6, wherein said
normalized standard deviation S.sub.n is less than or equal to
0.002.
8. A strengthened glass sheet according to claim 6, wherein said
normalized standard deviation S.sub.n is less than or equal to
0.001.
9. A strengthened glass sheet, the sheet comprising first major
surface; a second major surface opposite the first major surface
and separated from the first major surface by a thickness t when
expressed in mm; a length of l when expressed in mm of at least 10;
a width of w when expressed in mm of at least 10; an interior
region located between the first and second major surfaces; and an
outer edge surface extending between and surrounding the first and
second major surfaces such that the outer edge surface defines a
perimeter of the sheet; wherein the sheet is thermally strengthened
such that at the first major surface is under compressive stress;
wherein a normalized standard deviation S.sub.n S n = s x _
##EQU00005## of membrane stress measurement samples taken through
the first and second major surfaces 12, 14 the sheet 10 in a series
distributed equally in the x and y directions, but not within a
distance of 2.5 times the thickness of the sheet to the outer edge
surface 16, for number of samples N=100, is less than or equal to
0.02.
10. A strengthened glass sheet according to claim 9, wherein said
normalized standard deviation S.sub.n is less than or equal to
0.002.
11. A strengthened glass sheet according to claim 9, wherein said
normalized standard deviation S.sub.n is less than or equal to
0.001.
12. A strengthened glass sheet according to claim 9, wherein the
sheet has a characteristic 2D autocorrelation matrix c(x,y) given
by c(x,y)=F.sup.-1(F(g){circumflex over (F)}(g)) where F is a 2D
Fourier transform and represents the complex conjugate operation
and g is a high pass filtered data array given by
g(x,y)=F.sup.-1(F(f)(1-F(h))) where h is a spatial 2D low pass
filter array andfis a square data array of Shear 0 and Shear 45
data, taken over an area away from any birefringence edge effects
on the sheet, wherein an autocorrelation peak maximum width of the
matrix c(x,y) at 40% of peak height, for the c(x,y) matrices from
both the Shear 0 and Shear 45 data, is between 1 and 5 mm.
13. The sheet according to claim 12 wherein the autocorrelation
peak maximum width of the matrix c(x,y) at 40% of peak height, for
the c(x,y) matrices from both the Shear 0 and Shear 45 data, is
between 1 and 4 mm.
14. The sheet according to claim 12 wherein the autocorrelation
peak maximum width of the matrix c(x,y) at 40% of peak height, for
the c(x,y) matrices from both the Shear 0 and Shear 45 data, is
between 1 and 3 mm.
15. The strengthened glass sheet according to claim 9, wherein the
first major surface of the sheet has a roughness, measured over an
area on the first major surface of 10 .mu.m.times.10 .mu.m, is in
the range of from 0.05 nm to 0.5 nm Ra
Description
[0001] This application claims the benefit of priority of U.S.
Provisional Application No 62/289,334, filed on Jan. 31, 2016, and
U.S. Provisional Application No. 62/428,531, filed on Dec. 1, 2016
the contents of which are relied upon and incorporated herein by
reference in their entirety.
[0002] This application is related to and hereby incorporates
herein by reference in full the following applications: Provisional
Application Ser. No. 62/288,177 filed on Jan. 28, 2016, U.S.
Provisional Application Ser. No. 62/288,615 filed on Jan. 29, 2016,
U.S. Provisional Application Ser. No. 62/428,142 filed on Nov. 30,
2016, and U.S. Provisional Application Ser. No. 62/428,168, filed
on Nov. 30, 2016, U.S. Provisional Application Ser. No. 62/288,851,
filed on Jan. 29, 2016, U.S. application Ser. No. 14/814,232, filed
on Jul. 30, 2015; U.S. application Ser. No. 14/814,181, filed on
Jul. 30, 2015; U.S. application Ser. No. 14/814,274, filed on Jul.
30, 2015; U.S. application Ser. No. 14/814,293, filed on Jul. 30,
2015; U.S. application Ser. No. 14/814,303, filed on Jul. 30, 2015;
U.S. application Ser. No. 14/814,363, filed on Jul. 30, 2015; U.S.
application Ser. No. 14/814,319, filed on Jul. 30, 2015; U.S.
application Ser. No. 14/814,335, filed on Jul. 30, 2015; U.S.
Provisional Application No. 62/031,856, filed Jul. 31, 2014; U.S.
Provisional Application No. 62/074,838, filed Nov. 4, 2014; U.S.
Provisional Application No. 62/031,856, filed Apr. 14, 2015; U.S.
application Ser. No. 14/814,232, filed Jul. 30, 2015; U.S.
application Ser. No. 14/814,181, filed Jul. 30, 2015; U.S.
application Ser. No. 14/814,274, filed Jul. 30, 2015; U.S.
application Ser. No. 14/814,293, filed Jul. 30, 2015; U.S.
application Ser. No. 14/814,303, filed Jul. 30, 2015; U.S.
application Ser. No. 14/814,363, filed Jul. 30, 2015; U.S.
application Ser. No. 14/814,319, filed Jul. 30, 2015; U.S.
application Ser. No. 14/814,335, filed Jul. 30, 2015; U.S.
Provisional Application No. 62/236,296, filed Oct. 2, 2015; U.S.
Provisional Application No. 62/288,549, filed Jan. 29, 2016; U.S.
Provisional Application No. 62/288,566, filed Jan. 29, 2016; U.S.
Provisional Application No. 62/288,615, filed Jan. 29, 2016; U.S.
Provisional Application No. 62/288,695, filed on Jan. 29, 2016;
U.S. Provisional Application No. 62/288,755, filed on Jan. 29,
2016.
FIELD
[0003] This disclosure relates to generally to improved thermally
tempered glass and more specifically to thermally strengthened
glass sheets having high homogeneity of membrane stresses.
BACKGROUND
[0004] Commonly-assigned U.S. Pat. No. 9,296,638 (the '638 patent)
entitled "Thermally Tempered Glass and Method and Apparatuses for
Thermal Tempering of Glass" discloses methods and apparatuses for
heating and/or thermally tempering glass sheets. The contents of
the '638 patent are relied upon and incorporated herein by
reference in their entirety for purposes of U.S. law.
DEFINITIONS
[0005] The phrases "glass sheet(s)" and "glass ribbon(s)" are used
broadly in the specification and in the claims and include sheet(s)
and ribbon(s) that comprise one or more glasses and/or one or more
glass-ceramics, as well as laminates or other composites that
include one or more glass and/or one or more glass-ceramic
components. The phrase "glass sheet(s)" is used to refer to glass
sheet(s) and glass ribbon(s) collectively. "Glass" includes glass
and materials known as glass ceramics.
SUMMARY
[0006] The present disclosure provides additional features or
enhancements relative to the methods and apparatuses for the
production of thermally strengthened glass of the '638 patent
which, together with the methods and apparatuses of the '638 patent
provide for the production of thermally strengthened glass having
improved homogeneity of membrane stress.
[0007] According to embodiments, a strengthened glass sheet has
first major surface, a second major a thickness t when expressed in
mm between the major surfaces; a length of l when expressed in mm
of at least 10; a width of w when expressed in mm of at least 10;
an interior region located between the first and second major
surfaces; and an outer edge surface extending between and
surrounding the first and second major surfaces such that the outer
edge surface defines a perimeter of the sheet; wherein the sheet is
thermally strengthened such that at the first major surface is
under compressive stress; the sheet having an a characteristic 2D
autocorrelation matrix c(x,y) given by
c(x,y)=F.sup.-1(F(g){circumflex over (F)}(g)) where F is a 2D
Fourier transform and represents a complex conjugate operation and
g is a high pass filtered data array given by
g(x,y)=F.sup.-1(F(f)(1-F(h))) where h is a spatial 2D low pass
filter array and f is a square data array of Shear 0 and Shear 45
data, taken over an area away from any birefringence edge effects
on the sheet, wherein an autocorrelation peak maximum width of the
matrix c(x,y) at 40% of peak height, for the c(x,y) matrices from
both the Shear 0 and Shear 45 data, is between 1 and 5 mm.
[0008] According to embodiments, the autocorrelation peak maximum
width of the matrix c(x,y) at 40% of peak height, is between 1 and
4 mm, 1 and 3 mm, or even 1 and 2 mm or less.
[0009] According to embodiments, the Ra roughness, measured over an
area on the first major surface of 10 .mu.m.times.10 .mu.m
according to the standard of ISO 19606, can be in the range of from
0.05 or 0.1 nm to 20, 4, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3 or even as
low as to 0.2 nm Ra.
[0010] According to embodiments, a normalized standard deviation
S,
S n = s x _ ##EQU00001##
of a sample of membrane stress measurement samples taken according
to ASTM F218 in transmission through the first major surface 12 of
the sheet 10 in a series distributed in the x and y directions for
number of samples N=100, is low (when edge effects of measuring too
close--i.e., within 2.5 times the thickness of the sheet to the
outer edge surface 16 are not included)--as low as 0.02, 0.015,
0.01, 0.005, 0.002, 0.001 or even lower.
[0011] The reference characters used are only for the convenience
of the reader and are not intended to and should not be interpreted
as limiting the scope of the invention. More generally, it is to be
understood that both the foregoing general description and the
following detailed description are merely exemplary of the
invention and are intended to provide an overview or framework for
understanding the nature and character of the invention.
[0012] Additional features and advantages of the invention are set
forth in the detailed description which follows, and in part will
be readily apparent to those skilled in the art from that
description or recognized by practicing the invention as
exemplified by the description herein. The accompanying drawings
are included to provide a further understanding of the invention,
and are incorporated in and constitute a part of this
specification. It is to be understood that the various features of
the invention disclosed in this specification and in the drawings
(which are not to scale) can be used individually and in any and
all combinations.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] FIG. 1 is a schematic cross sectional side view drawing of
an embodiment of a heat sink or source for heating or cooling a
glass sheet.
[0014] FIG. 2 is a schematic cross sectional side view drawing of
an embodiment of an apparatus for heating and then quenching glass
sheets.
[0015] FIG. 3 is a schematic cross-sectional plan view drawing of
an embodiment of a heat source.
[0016] FIG. 4 is a perspective view drawing of an sheet or sheet
comprising glass.
[0017] FIG. 5 is a schematic cross sectional side view drawing of
an embodiment of a heat sink or source.
[0018] FIG. 6 is a schematic cross sectional side view drawing of
another embodiment of a heat sink or source.
[0019] FIGS. 7A and 7B show a representative example result of 2D
autocorrelation of a non-uniform sample.
[0020] FIGS. 8A and 8B show a representative example result of 2D
autocorrelation of a highly uniform sample.
DETAILED DESCRIPTION
[0021] FIG. 1 is a schematic cross sectional side view drawing of
an embodiment of an arrangement of a pair of heat sinks or sources
Si/So for heating or cooling a glass sheet 10. Thin gaps 20 between
the sheet 10 and the heat sinks or sources Si/So contain a gas
through which heat is conducted to heat or cool the sheet 10 such
that at least 20% of the total heating or cooling is by conduction,
desirably 30, 40, 50, 60, and even 70, 80 or 90% or more. The sheet
10 is supported between the two sinks or sources Si/So by any
suitable and most preferably non-contact means, including such
alternatives as ultrasonic energy, electrostatic forces, but
preferably by gas bearings formed in the gaps 20 (comprising first
gap 20a and second gap 20b).
[0022] The sheet 10 can be stationary or in motion between the
sinks or sources Si/So. The sheet 10 can be smaller (in one
dimension or both) than the extent of the sinks or sources Si/So or
larger (preferably in one dimension only, in which case continuous
processing in the larger direction is preferred). The sheet 10 can
be multiple sheets heated or cooled together at the same time. The
gas in the first and second gaps 20a and 20b can be the same or
different, and both or either can be gas mixtures or essentially
pure gases. Generally, gases or gas mixtures with relatively higher
thermal conductivity are preferred. Use of gas bearings allows
robustly maintaining the desired size of the gaps 20a and 20b,
which enables relatively homogeneous heat transfer rates over all
areas of the gaps 20, in comparison to cooling or heating by direct
contact with liquids or with solids, and in comparison to cooling
by forced air convection.
[0023] As represented in the diagrammatic cross section of FIG. 2,
a thermal tempering or strengthening apparatus 8 generally includes
both a heating zone 30 and a cooling zone 40, and both can be in
the form of a pair of heat sources So or a pair of heat sinks Si,
separated from the sheet by thin gas gaps 20 as in FIG. 1. As an
alternative, the heating zone may be in the form of a conventional
furnace or oven rather than the thin-gap arrangement of heat
sources So shown here. In general terms, heating zone 30 heats the
glass sheet(s) to a temperature sufficient for thermal
strengthening, and the cooling zone 40 lowers the temperature of
the sheet(s) by removing heat through the surfaces of the sheet(s)
at a rate sufficient and for a sufficient time to achieve a desired
level of thermal strengthening when the sheet(s) are (later)
finally at ambient temperatures. A sheet 10 is heated to a
sufficient temperature for generating temper effects (generally
between the glass transition point and the softening point of the
glass), and is cooled in the cooling zone. Transport may be by any
suitable means.
[0024] FIG. 4 shows a perspective view of the sheet 10 comprising
glass, which includes a first major surface 12, a second major
surface 14 opposite the first (obscured in the view of FIG. 3), an
interior region I located between the first and second major
surfaces, and an outer edge surface 16 extending between and
surrounding the first and second major surfaces such that the outer
edge surface defines the perimeter of the sheet. x-y-z coordinates
are shown for ease of reference, with z in the thickness
direction.
[0025] Gas bearings, as alternative embodiments, may take either of
the forms shown in FIGS. 5 and 6. FIG. 5 is a schematic cross
sectional side view drawing of one embodiment of a heat sink or
source Si/So, and FIG. 6 is a schematic cross sectional side view
drawing of another embodiment of a heat sink or source Si/So. In
both of these embodiments, the circular structures are thermal
control structures 34, such as cartridge heaters if the embodiment
is a heat source So, or such as coolant passages if the embodiment
is a heat sink Si. The embodiment of FIG. 5 employs discrete holes
36 through which gas can be fed from a plenum 38. The embodiment of
FIG. 6 includes a porous structure 42 through which gas can
likewise be fed from a plenum 38, with the effect that the gas is
emitted essentially from every portion of the surface 44 of the
porous structure 42.
[0026] Because of the non-contact treatment and handling possible
in the thermal strengthening apparatus of FIG. 2, by using gas
bearings such as in FIGS. 5 and 6 or by other suitable non-contact
means, the first major surface 12 of the sheet 10 can have very low
roughness, achieved by preserving the as-floated quality of the
"air side" of float glass, or the as-drawn quality of either side
of fusion-drawn glass. The Ra roughness, measured over an area on
the first major surface of 10 .mu.m.times.10 .mu.m according to the
standard of ISO 19606, can be in the range of from 0.05 or 0.1 nm
to 20, 4, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3 or even as low as to 0.2 nm
Ra. The self-restoring or self-centering effects of opposing gas
bearings can also assist in keeping thin glass sheets flat, even
very thin sheets. Thin sheets with thicknesses within in the range
of from 0.1, 0.2 or 0.5 mm to 3, 2.8, 2.6, 2.4, 2.2, 2.0, 1.8, 1.6,
1.4, 1.2, 1.1, 1, 0.9, 0.8, 0.7, 0.6 mm can be processed, as well
as thicker sheets.
[0027] Achieving uniformity of cooling effects in the cooling zone
40 over the area of the sheet 10 requires maintaining the desired
size of the gaps 20. It has also been found that maintaining the
homogeneity of the gas in the gaps 20a, 20b within the cooling zone
is important. If different gases are used in the heat source So
gaps and the heat sink Si gaps, gas can be drawn away by a suitable
suction or vacuum means at a position between the sources So and
the sinks Si, as indicated by the arrows A in FIG. 2, so that the
differing gases do not mix within the heat sinks Si of the cooling
zone (or within the heat sources So). Alternatively and optionally,
a transition zone such as is disclosed in the '638 patent,
positioned between the heating and cooling zone, can include a feed
of the same gas as in the cooling zone and can physically isolate
the heating zone gas from the cooling zone gas in the case that
they are different. Interestingly, and in contrast to forced
convective gas tempering, when the gases are the same and
conduction is the dominating heat transfer mode, any hot gas
traveling with the sheet 10 from hot zone 30 to cold zone 40 is not
a very significant factor in the process, since the thermal mass of
the gas is negligible relative to the effects of conduction.
[0028] For good homogeneity of heat transfer rates during heating
and resulting homogeneous temperature profiles and final properties
of sheet 10, it is also desirable to provide a heat source So
providing for a non-uniform distribution of heating energy. FIG. 3
shows diagrammatic cross sectional plan view of a heat source So
such as those of FIGS. 1 and 2, having such a non-uniform
distribution of heating energy in the form of cartridge heaters 32
distributed within the heat source So. A first spacing S1 of the
cartridge heaters near the left and right edges of the heat source
So in the figure is closer than a second spacing S2 of the
cartridge heaters in the more central region of the heat source So.
This has the effect, desired in most circumstances, of balancing
thermal losses to the ambient environment at the left and right
edges of the heat source So. Similarly, the windings within the
cartridge heaters 32 can have a first average winding density W1
near the edges (top and bottom in the figure) of the heat source So
greater than a second average winding density W2 in the more
central region of the heat source So.
[0029] With good control of the thermal profile of the sheet just
before cooling, such as may be achieved by the heat source So of
FIG. 3 or by other suitable means, and with steps taken to prevent
unwanted gas mixing in the heat sink Si, as described in connection
with FIG. 2 or by other suitable means, thermally strengthened
sheets comprising glass and/or glass ceramic can be produced having
very good quality, especially relative to the achieved
strengthening as a function of glass thickness and glass
properties. In particular, the improved properties can include
improved homogeneity of membrane stresses.
[0030] For example, an sheet processed according to this disclosure
in combination with the disclosure of the '638 patent can achieve a
desirable low deviation of membrane stress, such that a normalized
standard deviation S.sub.n
S n = s x _ ( 1 ) ##EQU00002##
of a sample of membrane stress measurement samples taken according
to ASTM F218 in transmission through the first major surface 12 of
the sheet 10 in a series distributed in the x and y directions for
number of samples N=100, is low (when edge effects of measuring too
close--i.e., within 2.5 times the thickness of the sheet to the
outer edge surface 16 are not included)--as low as 0.02, 0.015,
0.01, 0.005, 0.002, 0.001 or even lower.
Membrane Stress Cross-Correlation Analysis
[0031] Measurement
[0032] A full-field polarimeter is used to make optical
birefringence measurements, through the thickness of the sample, of
retardation magnitude and slow-axis azimuth. The optical axis of
the polarimeter is aligned to the desired coordinate axis of the
sample. Multiple point measurements are made on an equal spaced XY
grid, so that a 2D map of birefringence is generated for the
sample. Grid spacing is sufficiently small so that the number of
steps in X and Y is many, for example, at least 100 in both X and Y
(after data from within 2.5 times sheet thickness of the edge is
excluded) is generally adequate for the test: more is desirable to
improve resolution but generally will not significantly impact
results. The grid size is also selected to be large enough
spatially to capture any spatially periodic features in the
data.
[0033] Data Processing
[0034] First, the optical birefringence values of magnitude and
azimuth are converted into the two shear stress components of Shear
0 ("S0") and Shear 45 ("S45") by the equations mcos(2az) and
msin(2az), respectively, as understood by those of skill in the art
of stress calculation through birefringence measurement. S0 and S45
may be calculated directly by the software of an instrument which
also first measures the multiple birefringence values in X and Y,
such as a grey-field polarimeter ("GFP") from Stress Photonics USA.
The results of this operation are two 2D arrays, one of S0 values
and the other of S45 values. S0 and S45 typically both have units
of nanometers, and both can be treated as scalar values for the
purposes of direct mathematical arithmetic.
[0035] As understood by those of skill in the art, if desired for
purposes of visualization or other analysis, the S0 and S45 values
may be converted into the in-plane components of principal stress,
S1 and S2. The results of this operation are two 2D arrays, one of
S1 values and the other of S2 values.
[0036] Data Analysis: 2D Autocorrelation Lengths
[0037] For input into this analysis, the two 2D arrays of S0 and
S45 are used. For each of the 2D arrays separately, we: (1) Extract
a sub-array dataset in which the number of columns and rows are
equal (i.e., the sub-array is square). The extraction area should
be away from the sample edge (by at 2.5 times the sheet thickness,
preferably 3 times according to one embodiment, 4 times according
to another) in order to avoid edge effects in the measured data. As
mentioned, the sub-array dataset must have a minimum number of rows
and columns, at least 100 each, so that the subsequent mathematical
operations can be robustly applied. (2) Filter the data through a
2D high-pass spatial filtering process to remove spatial
frequencies less than about one cycle per array width, effectively
removing spatial variations such as slope or tilt of the data. This
may be performed in two steps, namely, (a) apply a 2D low-pass
spatial filter to the sub-array dataset to remove the high
frequency components above a desired cutoff frequency, and (b)
subtract from the unfiltered sub-array dataset the filtered
sub-array dataset, to generate the high-pass filtered sub-array
dataset. (4) Perform a 2D auto-correlation on the high-pass
filtered sub-array dataset.
[0038] To describe these steps formulaically, we can represent our
starting 2D array (for both S0 and S445 date sets) by f(x,y), our
high pass array by g(x,y), our spatial 2D low pass filter array by
h(x,y), and is our autocorrelation array by c(x,y). The filter
h(x,y) is defined as
h ( x , y ) = e - ( x 2 + y 2 ) l n ( 2 ) 10 2 ( 2 )
##EQU00003##
within a square -1/2W.sub.f.ltoreq.x,y.ltoreq.1/2W.sub.f and zero
outside the square, where W.sub.f is the filter width. Filter
components are normalized to sum to 1 so that the filter produced
no gain. We use F( ) and F.sup.-1( ) to denote 2D Fourier and 2D
inverse Fourier transforms, respectively. Also, for this
discussion, "" will represent array multiplication and " " will
represent the complex conjugate operation. Then g(x,y) is given
by
g(x,y)=F.sup.-1(F(f)(1-F(h))) (3)
and the 2D auto correlation matrix is given by
c(x,y)=F.sup.-1(F(g){circumflex over (F)}(g)) (4)
The resulting 2D autocorrelation sub-array dataset c(x,y) will
contain a central peak with relative amplitude of 1. The
cross-section of this peak will not generally be circular, but
rather elliptical in shape with minimum and maximum diameters in
units of distance. At a desired relative amplitude level (height)
(e.g., at 0.4), the minimum and maximum diameters of the central
peak (in whatever direction they lie) can be extracted to record as
autocorrelation lengths.
[0039] FIGS. 7A and 7B show a representative example result of 2D
autocorrelation of a non-uniform sample, with a plane view of the
data shown in FIG. 7B, and an oblique view of the same data in FIG.
7A. The unit axes in the plane are in millimeters, with the cross
correlation peak on a unit scale of 1. The central peak and its
varying diameter is particularly visible particularly in FIG. 7A.
FIGS. 8A and 8B show a representative example result of 2D
autocorrelation of a highly uniform sample, with a plane view of
the data shown in FIG. 7B, and an oblique view of the same data in
FIG. 7A. The central peak, which is almost as narrow as the
resolution of the data allows, is particularly in FIG. 7A.
[0040] Comparison of multiple sheets of the present disclosure with
multiple samples of sheets produced using conventional forced-air
convention cooling has shown that autocorrelation peak maximum
width at 40% of peak height (at height of 0.4), for both the Shear
0 and Shear 45 data sets, is between 1 and 5 mm, indicating
relatively weak periodic non-uniformity in the birefringence and
membrane stress of the sheet. Sheets produced using conventional
forced-air convention cooling have significantly larger
autocorrelation widths at height of 0.4, indicating stronger
periodic non-homogeneity in the retardance and membrane stress of
the sheet.
[0041] A variety of modifications that do not depart from the scope
and spirit of the invention will be evident to persons having
ordinary skill in the art from the foregoing disclosure.
* * * * *